A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness
Abstract
Entanglement and nonlocal non-stabilizerness are distinct quantum resources encoded in the Schmidt spectrum of a bipartite pure state. For qubit systems, we establish a universal quadratic constraint on their simultaneous allocation, governed by the minimum number of logical qubits required on each side to encode the occupied Schmidt support. Additional spectral constraints reveal a strong asymmetry in their allocation with the Entanglement that can exhaust the logical capacity, whereas the maximal nonlocal non-stabilizerness grows only logarithmically with it. For a tensor-network cut crossed by a single separating virtual edge, the logical capacity is determined by the occupied bond dimension. We further derive a one-sided certificate for the resources of the untruncated state from a retained Schmidt spectrum and its discarded weight. For small discarded weight, the resulting corrections are linear in that weight. These results connect a universal resource budget to resource-aware control of tensor-network truncations.
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BibTeX
@misc{giampaolo2026universal,
title = {{A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness}},
author = {Salvatore Marco Giampaolo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31841},
eprint = {2609.31841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31841},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness
AU - Salvatore Marco Giampaolo
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31841
UR - https://arxiv.org/abs/2609.31841
AB - Entanglement and nonlocal non-stabilizerness are distinct quantum resources encoded in the Schmidt spectrum of a bipartite pure state. For qubit systems, we establish a universal quadratic constraint on their simultaneous allocation, governed by the minimum number of logical qubits required on each side to encode the occupied Schmidt support. Additional spectral constraints reveal a strong asymmetry in their allocation with the Entanglement that can exhaust the logical capacity, whereas the maximal nonlocal non-stabilizerness grows only logarithmically with it. For a tensor-network cut crossed by a single separating virtual edge, the logical capacity is determined by the occupied bond dimension. We further derive a one-sided certificate for the resources of the untruncated state from a retained Schmidt spectrum and its discarded weight. For small discarded weight, the resulting corrections are linear in that weight. These results connect a universal resource budget to resource-aware control of tensor-network truncations.
ER -